"thing that mashes," c.1500, agent noun from mash (v.). Meaning "would-be lady-killer" is from 1875, American English, perhaps in use from 1860, probably from mash (v.) on notion either of "pressing one's attentions," or of "crushing someone else's emotions" (cf. crush).

He was, to use a Western expression, a 'regular heart-smasher among the women; and it may not be improper to state, just here, that no one had a more exalted opinion of his capabilities in that line than the aforesaid 'Jo' himself. ["Harper's New Monthly Magazine," March 1861]

He had a weakness to be considered a regular masher of female hearts and a very wicked young man with the fair sex generally, but there was not a well-authenticated instance of his ever having broken a heart in his life, nor likely to be one. [Gilbert A. Pierce, "Zachariah, The Congressman," Chicago, 1880]Also in use late 19c were mash (n.) "a romantic fixation, crush" (1884); mash (v.) "excite sentimental admiration" (1882); mash-note "love letter" (1890).(Src: etymonline.com)

Since mash and masher have such non-literal meanings as you have discussed, what could one of a mind to create slang do with the famous British lunch of bangers and mash (sausage and mashed potatoes)? I blush to imagine.

The English have beaten you to the punch on this, I have watched at least two Brit comedy routines that build to a comedic requirement for a cigarette. Naturally, served for dessert is spotted dick.

There is a Irish pub the Burren in Davis Square, Somerville, MA the servers good bangers & mash. Also, the James Gate in Jamaica Plain, Boston, MA does it good too. I had spotted dick in London twice, one version was terribly dry, the other was okay. I think the first they left the lard out, and the currants were substituted by chocolate. Wonder if B&M Baked Beans means bangers & mash... I know it means Burnham & Morrill. I did grow up in Maine, and drive past the factory in Portland, ME all the time.

We have what I thought was an English like pub near my home, and I intended to visit it until I was warned that it was really only a front for illegal gambling. Someone quipped, "Did you ever hear anyone say, let's get some English food?" Some Americans may dis English food but, having spent a lot of time in England, I can say that most English food is very good. Now French food in England or in America is another topic, and I have never been to France. I am afraid to go. Ugly American disdain and such. I am sensitive as you all know.

Epcot has a section for "foreign" restaurants. One I ate in was an English pub. I ordered strak and kidney pie, which I had read of a good deal, but I was disappointed. The kidney part tasted like bad liver. While I love liver, this just didn't make the boat. Bangers and mash sounds great though.

After the holidays I may write a long scholarly treatise on the word mash. Right now I am too busy eating Christmas tamales (masa and a filling, usually pork, steamed in a corn shuck). La Navidad es una época del año especialmente alegre y divertida, y'all.